signal flowchart

impulse invariance

bilinear transformation

merical approximations introduced in the representations of variables can easily

produce diverging signals that are difficult to control.

version

the design of a discrete-time system starts from the description of a physical

continuous-time system by means of differential equations and constraints. This

description of an analog system can itself be derived from the simplification

of the physical reality into an assembly of basic mechanical elements, such as

springs, dampers, frictions, nonlinearities, etc. . Alternatively, our continuous-

time physical template can result from measurements on a real physical system.

In any case, in order to construct a discrete-time system capable to reproduce

the behavior of the continuous-time physical system, we need to transform the

differential equations into difference equations, in such a way that the resulting

model can be expressed as a signal flowchart in discrete time.

formation.

discrete-time system is a uniform sampling of the impulse response h

according to

since the design stems from specifications for the discrete-time filter, and the

conversion to continuous time is only an intermediate stage. Since one should

introduce 1/T when going from discrete to continuous time, and T when return-

ing to discrete time, the overall effect of the constant is canceled. Vice versa, if

we start from a description in continuous time, such as in physical modeling,

the constant T should be considered.

of the continuous-time system, with a repetition period equal to F

discrete and continuous, can be identical in the base band only if the continuous-

time system is bandlimited. If this is not the case (and it is almost never the

case!), there will be some aliasing that introduces spurious components in the